Systems and methods for evaluating vessels

ABSTRACT

Disclosed are systems and methods for evaluating body vessels. Images of the vessel are captured, analyzing to generate a three-dimensional model of the vessel, and the data associated with the three-dimensional model is analyzed. In cases in which the vessel is a coronary artery, the vessel model can be analyzed to determine the vulnerability of plaques within the artery to rupture. In some embodiments, the images are optical coherence tomography images. In some embodiments, the images are captured with an optical catheter that includes a tracking device. In some embodiments, the analysis includes flow and/or structural analysis.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to copending U.S. provisional application Ser. No. 60/773,486, entitled, “Optical Apparatuses and Methods,” filed Feb. 15, 2006, and U.S. utility application Ser. No. 11/417,599, entitled, “Optical Probes For Imaging Narrow Vessels Or Lumens,” filed May 4, 2006, both of which are hereby incorporated by reference in their entirety.

BACKGROUND

Cardiovascular disease (CVD) is the single most common cause of fatality in the developed world. In 2005, the American Heart Association estimated that approximately 865,000 Americans will acquire a new acute coronary syndrome (ACS) each year and that another 700,000 will have a stroke, with similar pathophysiology. From the pool of patients with acute coronary syndrome, about 22 percent of men and about 46 percent of women develop disabling heart failure within the following 6 years. It is expected that by the year 2020, cardiovascular disease will claim 25 million deaths annually worldwide with coronary artery disease representing half of those deaths.

Arterial plaque rupture is the most common complication associated with atherosclerosis, and accounts for approximately 70% of fatal coronary events. The transition into unstable plaques is characterized by the presence of active inflammation (monocyte/macrophage infiltration), thinning of the fibrous cap of the plaque, development of a large lipid necrotic core, and endothelial denudation with superficial platelet aggregation. Although such a condition is serious, it can be treated, at least in some cases, with aggressive therapy intended to prevent a catastrophic vascular event if the existence and location of the vulnerable plaque are detected.

Techniques currently exist that are used in an attempt to detect vulnerable plaques. Unfortunately, such plaques often may not be detected by such techniques for various reasons, including poor resolution of the imaging modality, slow system response, and complexity. Thus, the practice of such techniques may not result in the detection of plaques that, if otherwise detected, could possibly be treated. It can therefore be appreciated that one goal is to develop systems and methodologies that would enable such detection, especially for real-time or near real-time applications. If such systems and methodologies could be developed, they would have a major impact on morbidity and mortality related to atherosclerotic disease.

SUMMARY

Disclosed are systems and methods for evaluating body vessels. In one embodiment, a system and a method relate to capturing optical coherence tomography (OCT) images of the vessel, analyzing the OCT images to generate a three-dimensional model of the vessel, and conducting analysis on data associated with the three-dimensional model.

In another embodiment, a system and a method relate to capturing images of the vessel by an optical catheter positioned within the vessel, simultaneously determining a position and orientation of the catheter with information generated by a tracking device of the catheter, analyzing the images to generate a three-dimensional model of the vessel, and conducting analysis on data associated with the three-dimensional model.

In a further embodiment, a system and method relate to capturing images of the vessel, analyzing the images to generate a three-dimensional model of the vessel, and conducting analysis on data associated with the three-dimensional model, the analysis including flow analysis in relation to fluid flow through the vessel and structural analysis in relation to walls of the vessel.

In one embodiment, an optical catheter includes an internal optical system configured to capture images of a vessel in which the catheter is positioned, and a tracking device that determines the position and orientation of the catheter within the vessel simultaneous of image capture.

BRIEF DESCRIPTION OF THE FIGURES

The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. In the drawings, like reference numerals designate corresponding parts throughout the several views.

FIG. 1 is a block diagram of a device that comprises an embodiment of a system for evaluating a vessel.

FIG. 2 is a flow diagram of an embodiment of a method for evaluating a vessel.

FIG. 3 is a perspective view of an embodiment of an optical catheter that can be used to capture image data relating to a vessel.

FIG. 4 is a side view of the optical catheter of FIG. 3 that shows an internal optical system of the catheter.

FIGS. 5A and 5B illustrate use of the optical catheter shown in FIGS. 3 and 4 within a vessel.

FIG. 6 is an example three-dimensional body reconstruction of a coronary artery segment.

FIG. 7 is a cross-section of the coronary artery of FIG. 6 taken at plane A of FIG. 6.

FIG. 8 is an example three-dimensional grid reconstruction of a coronary artery segment.

FIG. 9 is a flow diagram of an embodiment of a method for acquiring and analyzing images of a vessel.

FIG. 10 is a further example three-dimensional grid reconstruction of a coronary artery segment.

FIG. 11 shows a velocity field determined at four longitudinal cross-sections of the lumen of the coronary artery segment of FIG. 10 taken at 45° intervals.

FIG. 12 shows a distribution of wall shear stress for the coronary artery segment of FIG. 10.

FIG. 13 shows a distribution of wall shear stress gradient for the coronary artery segment of FIG. 10.

FIG. 14 shows a distribution skin friction coefficient for the coronary artery segment of FIG. 10.

FIG. 15 is an example representation of a coronary artery segment including the artery lumen and the arterial wall/plaque structure.

FIG. 16 illustrates a predicted flow pattern for an artery segment.

FIG. 17 illustrates distributions of shear stress for 20%, 40%, and 70% stenosis.

FIGS. 18A and 18B illustrate predicted stress distributions obtained from structural analysis.

FIGS. 19A and 19B illustrate maximum shear stress and circumferential stress within the arterial wall/plaque structure.

FIGS. 20A and 20B illustrate stress ratio distributions R₁ and R₂.

FIGS. 21A and 21B illustrate the stress ratio distributions R₃ and R₄.

FIG. 22 illustrates a characterization of stenotic plaque vulnerability.

DETAILED DESCRIPTION Introduction

As described above, current technologies may be ineffective in enabling identification of vulnerable arterial plaques. Given that such plaques could be treated if detected, it can be appreciated that there is a need for systems and methods that could be used for early identification of vulnerable plaques.

In the following, described are various embodiments of systems and methods for evaluating vessels, such as human coronary arteries. As described below, images of an artery can be captured with imaging apparatus and used to identify plaques within the artery. In cases in which the images are high-resolution images, for example when optical coherence tomography (OCT) is used to capture the images, the images may reveal great detail as to the structure of the plaques and, therefore, may provide reliable data for flow and structural analyses and provide an indication as to plaque vulnerability. As is also described below, the captured image data can be used to construct a three-dimensional reconstruction or model of the artery. In embodiments in which the image data is collected using an internal catheter, the construction of such a model can be greatly simplified through use of a tracking device that provides position and orientation information regarding the catheter. Once the three-dimensional model of the artery has been constructed, various analyses, such as fluid analysis and structural analysis, can be conducted to assist in the identification and/or evaluation of arterial plaques. In some embodiments, fluid and structural analyses are used concurrently to make a plaque vulnerability determination or otherwise characterize the plaque.

Although evaluation of coronary arteries is discussed in detail in this disclosure, it is to be appreciated that the disclosed systems and methods can be used to evaluate other arterial or non-arterial conditions. In addition, the disclosed systems and methods may be used in conjunction with other body vessels, or other biological or non-biological vessels as the case may warrant. Furthermore, although particular embodiments of systems and methods are described in the following, those embodiments are mere example implementations of the systems and methods and it is noted that other embodiments are possible. All such embodiments are intended to be within the scope of this disclosure. The terminology used in this disclosure is selected for the purpose of describing the disclosed systems and methods and is not intended to limit the breadth of the disclosure.

System and Method Overview

Beginning with FIG. 1, illustrated is a computer system 100 that includes a computer-readable medium in the form of computer memory 102. As will be appreciated from the following disclosure, the particular configuration of the computer system 100 and the memory 102 are not critical. By way of example, however, the computer system 100 comprises a desktop, laptop, or server computer that includes the computing and processing power necessary to conduct the data collection and manipulation described in the following. Although the computer system 100 can comprise a single computer, the system can, alternatively, comprise two or more such computers. For example, multiple networked computers can be used, if desired. Also by way of example, the memory 102 can comprise a combination of volatile and non-volatile memory components. For instance, the memory 102 may comprise one or more hard disks and one or more random access memory (RAM) components. In addition, the memory 102 can comprise read-only memory (e.g., Flash memory) and one or more removable memory components, such as a floppy disk, a CD-ROM, or a memory card.

Stored within memory 102 is an evaluation system 104. The evaluation system 104 comprises several modules that serve discrete purposes within the system during evaluation of a vessel. In the embodiment shown in FIG. 1, the system 104 includes an imaging acquisition module 106, an image analysis module 108, a flow analysis module 110, and a structural analysis module 112. Although the various modules 104-112 are illustrated in FIG. 1 as being independent, the modules can comprise part of a single program that is used to evaluate vessels. Accordingly, two or more of the modules 104-112 may be combined or otherwise linked with each other. As is further indicated in FIG. 1, the image acquisition module 106 can be coupled to imaging apparatus 114 that are used to capture images of the vessel.

The image acquisition module 106 comprises the logic that is used to control operation of the imaging apparatus 114 and/or collect and store images captured by the imaging apparatus. In some embodiments, the image acquisition module 106 also collects tracking data relevant to the image capture process. The nature of the image acquisition module 106 may depend upon the nature of the imaging apparatus 114. By way of example, the imaging apparatus 114 can comprise ultrasound imaging apparatus, optical coherence tomography (OCT) imaging apparatus, fluorescence spectroscopy imaging apparatus, magnetic resonance imaging (MRI) apparatus, a combination of those apparatuses, or other suitable imaging apparatus. An example part of one suitable imaging apparatus is described in relation to FIGS. 3 and 4 below.

The image analysis module 108 digitizes and processes the images captured with the imaging apparatus 114. In addition, the image analysis module 108 processes any tracking data that may have been collected during image acquisition. Through such processing, the image analysis module 108 quantifies morphologic information pertaining to the vessel including the luminal geometry and any vessel landmarks, such as plaque size and location. That data is then used by the image analysis module 108 to construct a three-dimensional reconstruction or model of the vessel.

The flow analysis module 110 is configured to use the morphologic information generated by the image analysis module 108 to delineate the flow domain for fluid flow studies, e.g., hemodynamics, within the vessel lumen. The spatial and/or temporal distribution of flow variables, such as velocity, pressure, wall shear stress, cell distribution, distribution of blood constituents, etc., can be obtained by the flow analysis module 110 through solution of appropriate governing equations, subject to appropriate boundary and initial conditions. The method of solution of those equations can be analytical or computational, and may rely on principles of computational fluid dynamics (CFD). The flow analysis module 110 may use numerical methods based on discretization of the reconstructed vessel into the computational grids or control volumes over which the governing equations are integrated and solved. In other embodiments, the flow analysis may utilize a meshless method which does not require discretization of the vessel into computational grids. In the case of arterial analysis, hemodynamic indices can be related to atherosclerosis plaque development and vulnerability. In addition, the flow analysis module can use special features to represent coronary interventional procedures such as stented arteries.

In embodiments in which the structural analysis module 112 is provided, that module can use the morphologic data generated by the image analysis module 108 to develop a stress analysis model within the arterial wall in order to investigate the coupled flow-structure interaction within the artery. Such analysis can be conducted simultaneous to the fluid flow analysis. Where the captured images are high-resolution images, a media-plaque boundary can be delineated that is used in the analysis. In some embodiments, the structural analysis module 112 can comprise an integral part of the flow analysis module 110. As is described in greater detail below, there may be two-way implicit coupling of the structural analysis module 112 and the flow analysis module 110 such that the analysis conducted by one module influences the other and vice versa. Specifically, variables calculated in the flow analysis module 110, such as pressure, can be provided to the structural analysis module 112, which calculates vessel and plaque deformation and stresses. The calculated deformations can then be used by the flow analysis module 110 to update the flow domain and recalculate using the new deformed geometry. Iterations can then be performed between the flow analysis module 110 and structural analysis module 112 until convergence is achieved.

FIG. 2 provides an overview of an example method for evaluating a vessel. Beginning with block 200, images of a vessel under evaluation are captured and stored. As described above, the vessel can, for example, comprise an artery which may have plaques that are vulnerable to rupture. In addition to the images, any tracking information relevant to the image acquisition can be collected, as indicated in block 202. In some embodiments, the tracking information comprises x-ray data collected during intravascular ultrasound (IVUS). In embodiments in which images are captured with an optical catheter, the tracking information can comprise position and orientation information collected from an internal tracking device of the catheter. In other embodiments, however, such “tracking” information is not needed. For example, when MRI is used, no separate tracking information is necessary given that MRI provides three-dimensional image data directly. As mentioned above, the images, and any tracking information that was captured, can be collected and stored by the image acquisition module 106.

Referring next to block 204, a three-dimensional reconstruction or model of the vessel is generated. The model can be generated by the image analysis module 108 using the images and any tracking information collected by the image acquisition module 106. At this point, as indicated in block 206, fluid flow analysis can be performed, for example by the flow analysis module 110 using data from the three-dimensional model. In some embodiments, structural analysis can also be performed, as indicated in block 208. As noted above, the structural analysis can be performed by the structural analysis module 112 simultaneous to the flow analysis. Notably, however, flow analysis alone may be sufficient in some cases to evaluate the vessel and any features of concern, such as plaques. In cases in which structural analysis is performed, however, results from the structural analysis may influence the flow analysis and vice versa. Therefore, as indicated in decision block 210, flow in the method may return to block 206 if all flow and structural analyses have not been completed. Operating in that manner, the flow and structural analyses can be performed in an iterative process.

Once all flow and/or structural analysis has been performed, one or more determinations can be made as to the vessel and/or any features of concern, such as plaques, as indicated in block 212. In some embodiments, the determinations can be made manually by a person skilled in interpreting the results of the various analysis that was conducted. In other embodiments, the determinations can be, at least partially, automated. For example, the flow analysis module 110 and/or the structural analysis module 112 can be further configured to provide a quantification of the likelihood of a given plaque rupturing. As described below, the quantification can, for example, take the form of an index that indicates the susceptibility of the plaque to such rupture.

Image Acquisition and Analysis

As described in the foregoing, images of the vessel under evaluation can be obtained using various imaging technologies. For example, one or more of ultrasound, OCT, fluorescence spectroscopy, and MRI can be used. One suitable method for collecting image data of an artery comprises intravascular ultrasound (IVUS), which is performed using an intravascular catheter that captures images of the artery from within the artery. A description of one method for performing IVUS and analyzing the captured data is described in a paper entitled “Reproducibility of Coronary Lumen, Plaque, and Vessel Reconstruction and of Endothelial Shear Stress Measurements In Vivo in Humans,” by Ahmet U. Coskun, Ph.D. et al., 2003 which is hereby incorporated by reference into the present disclosure. In that method, IVUS image data is obtained with simultaneous biplane coronary angiography (BCA) in which two, preferably orthogonal, frames of biplane angiograms are taken at the same instant of time. During image acquisition, an IVUS catheter is advanced into the target coronary artery and intracoronary nitroglycerin is administered. A diluted contrast solution is injected at sufficient concentration to allow the simultaneous visualization of the arterial lumen and the IVUS catheter core just before the IVUS pullback while BCA is performed. Images of both projections are digitally recorded for approximately 3 to 4 seconds at a rate of 15 frames per second.

The IVUS and BCA images are ECG-gated to obtain end-diastolic images, which are marked to guide the software algorithms. The calibration points, which are used to correct geometric distortions, the starting point of IVUS pullback, and the traces of IVUS catheter core and lumen are marked on the digital BCA images. On each IVUS image, 12 guide marks positioned 30° apart around the IVUS catheter core can be used to trace the lumen and the external elastic membrane (EEM) borders. The EEM is the discrete interface at the border between the media and the adventitia, and it is represented as a thin echolucent line on the IVUS image. The distance between the EEM and lumen borders define the plaque thickness (plaque plus media or atheroma thickness).

Fusion of the IVUS and BCA images is then performed to determine the three-dimensional arterial geometry. Briefly, the BCA images are first rectified using a calibration grid to correct the geometrical distortions that occur during imaging. The physical three-dimensional path of the IVUS transducer during pullback is determined using the corresponding angiographic projections in BCA. The reconstructed path of the IVUS catheter core serves as the stem on which the three-dimensional vessel geometry is built. The three-dimensional position of each ECG-gated IVUS frame is determined from the trajectory of the catheter pullback, the known speed of the mechanical IVUS pullback speed, and the ECG signal. The normal direction of each frame is determined from the corresponding tangential direction of the catheter core since the IVUS image is perpendicular to the core axis. The IVUS images are segmented to extract the boundary of lumen and EEM and are interactively edited as needed. The three-dimensional reconstruction is completed by positioning the lumen and EEM boundary along the IVUS path while correcting for rotation of the IVUS caused by twisting of the catheter. Approximately 200-400 IVUS images are used to recreate each arterial segment, depending on its length and the heart rate. Once the lumen is reconstructed using the acquired data, a portion of the reconstructed segment, which is free of significant side branches and available in both pullbacks, is selected as the segment of interest to be used in the flow and/or structural analyses.

A further example of performing IVUS/BCA and analyzing the captured data is described in a paper entitled “Reconstruction and Spatial Filtering of 3-D Geometry of Coronary Artery Segments,” by A. U. Coskun, Ph.D. et al., 2000, which is also hereby incorporated by reference into the present disclosure.

Although IVUS is a viable methodology for image acquisition, OCT provides advantages that are not realizable with IVUS. OCT, like ultrasound, produces images from backscattered “echoes,” but uses infrared (IR) or near infrared (NIR) light that is reflected from internal microstructures within tissues or other materials under evaluation. Interferometric techniques are then used to extract the reflected optical signals from the IR or NIR light used in OCT. The output, measured by an interferometer, is computer processed to produce high-resolution, real-time, cross-sectional or three-dimensional images of the tissue. The IR or NIR light is emitted from a high-intensity light source, such as a super-luminescent diode or a laser. By way of example, a Gaussian beam having a central wavelength of approximately 800 nanometers (nm) to 1500 nm can be used. Notably, video rates can be achieved in cases in which Fourier-domain OCT is performed.

Significantly, OCT provides higher resolution images than ultrasound and, therefore, provides more information about the structure and composition of the walls and plaques of an artery. More particularly, OCT can provide images that reveal the boundaries of the structural components of the vessel walls and plaque and therefore provides more information that is relevant to the evaluation of the vulnerability of the plaque to rupture.

For a detailed discussion of OCT as used in biological applications, reference can be made to a paper entitled “Optical Coherence Tomography (OCT),” by Ulrich Gerckens et al., 2003, which is hereby incorporated by reference into the present disclosure.

In some embodiments, OCT can be combined with two-photon fluorescence spectroscopy to obtain even more information about the artery and plaque composition. With appropriate tuning and focusing, IR or NIR light can be concentrated on microstructures of the artery and/or plaque so as to cause two-photon excitation of the microstructures that results in emission of fluorescent light.

Although BCA can be used to determine the position and orientation of an IVUS or OCT catheter and, therefore, the position and orientation of the images captured with the catheter, reliance upon BCA presents several disadvantages. First, BCA is expensive to perform and requires expensive and cumbersome equipment that is possessed by only a few hospitals. Second, it is potentially harmful to the patient given that the patient is exposed to a relatively large dose of radiation. In view of those drawbacks, it may be desirable in some embodiments to equip the catheter with a tracking device that automatically provides real-time information as to the position and orientation of the catheter while it captures images within the vessel.

FIG. 3 illustrates an optical probe or catheter 300 that can form part of the imaging apparatus 114 shown in FIG. 1. In the example embodiment of FIG. 3, the catheter 300 is an OCT catheter that incorporates microtracking capability. As shown in FIG. 3, the catheter 300 includes a generally cylindrical outer housing 302. The outer housing 302 is elongated and comprises a proximal end 304, a distal end 306, and an outer periphery 308 that extends between the two ends. In the illustrated embodiment, an imaging window 310 is provided along the outer periphery 308 adjacent the distal end 306 of the catheter 300. Visible through the imaging window 310 in FIG. 3 are components of an internal optical system of the catheter (see FIG. 4). The imaging window 310 extends along the circumference of the outer housing 302 so as to permit 360° viewing using the internal optical system.

The optical catheter 300 is dimensioned such that it may be used in narrow, for example small diameter, vessels. By way of example, the optical catheter 300 has an outer diameter of approximately 1 millimeter (mm) to 2 mm, and a length of approximately 20 mm from its proximal end 304 to its distal end 306.

Extending from the proximal end 304 of the optical catheter 300 is a flexible cord 312 that transmits light to and receives light signals from the internal optical system. The outer diameter of the cord 312 can be smaller than that of the housing 302, and the length of the cord can depend upon the particular application in which the catheter 300 is used. Generally speaking, however, the cord 312 is long enough to extend the catheter 300 to a site to be imaged while the cord is still connected to a light source (not shown) that transmits light through the cord to the catheter.

The materials used to construct the optical catheter 300 can be selected to suit the particular application in which it is used. In biological applications, biocompatible materials are used to construct the catheter 300. For example, the outer housing 302 of the catheter 300 can be made of stainless steel or a biocompatible polymeric material. The imaging window 310 can be made of a suitable transparent material, such as glass, sapphire, or a clear, biocompatible polymeric material. In some embodiments, the material used to form the imaging window 310 can also be used to form a portion or the entirety of outer housing 302.

The cord 312 can comprise a tube made of a resilient and/or flexible material, such as a biocompatible polymeric material. In some embodiments, the cord 312 can comprise a tube composed of an inner metallic shaft, coil, or braid, for example formed of stainless steel or nitinol, that is surrounded by an impermeable polymeric sheath. Such an embodiment provides additional column strength and kink resistance to the cord 312 to facilitate advancing the catheter 300 to the imaging site. In addition, the outer housing 302 and/or the cord 312 can be coated with a lubricious coating to facilitate insertion and withdrawal of the catheter 300.

FIG. 4 illustrates the interior 400 of the optical catheter 300. As shown in that figure, the catheter 300 houses an internal optical system 402. In the embodiment of FIG. 4, the optical system 402 comprises collimation optics including a collimating lens 404, axicon optics including an axicon lens 406, imaging optics including a first imaging lens 408 and a second imaging lens 410, and a mirror 412. Each of the collimating lens 404, axicon lens 406, and first imaging lens 408 are fixedly mounted within the housing 302 using appropriate mounting fixtures (not shown). Substantially any mounting fixtures that secure the lenses in place and that do not undesirably obstruct the transmission of light through the optical system 402 can be used. The second imaging lens 410 is fixedly mounted to the mirror 412 with a mounting arm 414 that extends from the mirror. The mirror 412 is, in turn, mounted to a shaft 416 of a micromotor 418 that is fixedly mounted adjacent the distal end 306 of the catheter 300. As shown in FIG. 4, the mirror 412 is mounted to the shaft 416 such that the mirror reflects light rays transmitted by the first imaging lens 408 toward the distal end 306 of the catheter 300, and reflects light rays transmitted back from the second imaging lens 410 toward the center of the catheter. Extending through the cord 312 is an optical waveguide 420, such as a single-mode optical fiber.

As is further shown in FIG. 4, the optical catheter 300 includes a tracking device in the form of a microtracker 422. The microtracker 422 provides real-time position and orientation information relating to the catheter 300 such that BCA is not required to determine the position and orientation of the images that are captured by the catheter. Such operation enables tracking of the catheter (e.g., catheter tip) in three-dimensional space in terms of X, Y, Z, yaw, pitch, and roll, thereby providing six degrees-of-freedom (6DOF).

By way of example, the microtracker 422 comprises the InertiaCube™ from InterSense. The InertiaCube™ is an integrated digital smart-sensor module based on micro-electro-mechanical systems (MEMS) technology involving no moving parts. By using sourceless (i.e., self-referenced) inertial sensors as a primary means of tracking motion, high update rates, desirable smoothness, predictive capability, and excellent immunity to various forms of external interference are possible. The InertiaCube™ also has integral solid-state magnetometers which sense components of earth's magnetic field along three perpendicular axes. Those magnetometer readings can be used as a digital electronic compass for correcting yaw drift in a sourceless orientation tracking modality. The technology used by the mircrotracker 422 is described in one or more of the following patents, each of which is hereby incorporated by reference into the present disclosure: U.S. Pat. No. 7,000,469, U.S. Pat. No. 6,922,632, U.S. Pat. No. 6,757,068, U.S. Pat. No. 6,681,629, U.S. Pat. No. 6,474,159, and U.S. Pat. No. 6,314,055.

With the above-described configuration, light from a high-intensity light source (not shown) is transmitted by the optical waveguide 420 to the collimating lens 404, to the first imaging lens 408, to the mirror 412, to the second imaging lens 410, and then out from the optical catheter 300 to the imaging site (not shown). When the micromotor 418 is activated, it rotates the shaft 416 and, therefore, axially rotates the mirror 412 and the second imaging lens 410 about a longitudinal central axis of the catheter 300 such that images can be captured substantially through 360° relative to that axis (i.e., the central axis extending from the proximal end 304 to the distal end 306). In addition, positional and orientation information is collected from the microtracker 422 for the purposes of interpreting the images captured by the catheter 300.

FIGS. 5A and 5B illustrate an example of use of the optical catheter 300 within a vessel 500. By way of example, the vessel 500 comprises a coronary artery. Referring first to FIG. 5A, the optical catheter 300 is shown positioned within the vessel 500. The catheter 300 could have been positioned by introducing the catheter into the vessel 300 using a needle or trocar (not shown). Once so introduced, the catheter 300 can be placed into position along the vessel 500 by advancing the catheter using the cord 312, for example in the direction indicated by arrow 502. The position and orientation information regarding the catheter 300 can be communicated, for example, to the image acquisition module 106 (FIG. 1) with the microtracker 422. Optionally, appropriate external visualization techniques, such as BCA or other x-ray imaging, can further be used to guide in the practitioner positioning the catheter 300 at the desired imaging site.

Once the optical catheter 300 is positioned as desired, the inner surface 504 and/or interior 506 of the wall that forms the vessel 500 can be imaged using the catheter. In FIG. 5A, the interior 506 of a bottom portion 508 of the vessel 500 is imaged with the catheter 300. As is apparent from that figure, the focal zone of the optical system 402 coincides with the wall interior 506 such that a given depth of the wall can be imaged without the need to adjust focus. By way of example, a resolution of approximately 5 microns (μm) can be achieved across a focal line or depth up to approximately 2 mm. For instance, in one embodiment, a resolution of 4.8 μm can be achieved for a focal line or depth of 1.5 mm.

Turning to FIG. 5B, the mirror 412 and second imaging lens 410 have been rotated 180° relative to their positions illustrated in FIG. 5A such that a second portion 510 of the vessel wall is imaged. Again, the wall interior 506 is imaged across a depth instead of at a discrete point such that dynamic focusing is unnecessary. Although only two portions 508 and 510 of the wall 506 have been illustrated as being imaged using the optical catheter 300, it is to be understood that the entire circumference of the vessel 500 can be imaged in the same manner due to the 360° rotation capability of the mirror 412 and the second imaging lens 410. Therefore, in some embodiments, images may be continually captured as the mirror 412 and second imaging lens 410 are continuously rotated or “swept” by the micromotor 418.

FIG. 6 is an example three-dimensional body reconstruction of a coronary artery segment 600. In FIG. 6, a portion of the artery segment 600 is shown removed to reveal an inner lumen 602 of the artery that is defined by the artery wall 604. FIG. 7 illustrates a cross-section of a portion of the segment 600 taken at plane A in FIG. 6. As can be appreciated from FIG. 7, the thickness of the artery wall 604 varies due to plaque 700 formation. In particular, the plaque 700 reduces the cross-sectional area of the lumen 602 so as to restrict the flow of blood through the artery.

FIG. 8 is an example three-dimensional grid reconstruction of a coronary artery segment 800, along with multiple cross-sections 802. As described below, such a grid reconstruction can be useful in conducting various analyses, such as flow analysis.

In view of the foregoing discussion, a method for acquiring and analyzing images can be described as provided in the flow diagram of FIG. 9. Beginning with block 900, images of the vessel under evaluation are captured with a catheter that is positioned within the vessel. By way of example, the catheter can have a configuration similar to that of the catheter 300 described in relation to FIGS. 3-5. Accordingly, in some embodiments, the catheter captures image data used to generate OCT and/or fluorescence spectroscopy images. Simultaneous to the image capture, the position and orientation of the catheter are determined by a microtracker provided within the catheter, as indicated in block 902.

The image data and the tracking information (i.e., position and orientation information) are collected, as indicated in block 904. Next, the image data and the tracking information are correlated, as indicated in block 906, such that a three-dimensional reconstruction or model of the vessel can be constructed, as indicated in block 908.

Flow Analysis

Once a three-dimensional model of the vessel has been constructed in the manner described above, the morphological information provided by the model is used to define the flow and/or structural domains for analyses of hemodynamics and structural evolution of the arterial wall-plaque assembly. The following describes an example method for performing flow analysis.

Local hemodynamic factors play a significant role in the development of atherosclerosis. It has increasingly been recognized that knowledge of the relationship between blood flow and disease pattern is essential to understanding the role of arterial fluid dynamics on the genesis and progression of atherosclerosis. While invasive animal studies can be used to follow dynamic plaque development, they do not provide local hemodynamic information and the techniques may not be applicable to humans. Experiments to elucidate the interactions between flow variables and endothelium can be readily conducted in vitro. However, understanding the clinical significance of those basic interactions depends on developing suitable methodologies for calculating and measuring intra-coronary flow in vivo, and on understanding the relationships between flow variables and the formation, morphology, and composition of complex plaque forms.

The nature and effect of the changing shear stresses existing along the longitudinal axis of the coronary artery have not been previously studied in detail. Nevertheless, such characteristics may be extremely important in identifying the natural history of a particular coronary plaque and its likelihood to become vulnerable and rupture. In the following technique, the relationships between local hemodynamic factors and atherogenesis and restenosis are evaluated. In particular, the technique is used to obtain the profiles of the endothelial shear stress and related flow indicators in the coronary artery segments of patients with cardiovascular disease.

In one embodiment, a reconstructed luminal segment is divided into N_(z) equal small slices each with thickness Δs, for use in generating computational grids. The intermediate slabs between the image frames are obtained by linear interpolation. Next, each slice is divided into N_(θ) equal intervals in the angular direction and NT intervals in the radial direction. A power law distribution is used for the radial divisions in order to concentrate grids in the important near-wall region. Finally, the slices are combined in three-dimensional space to form the computational mesh.

In other embodiments, only the locations of the boundaries of the reconstructed vessel are required. The internal points needed in conjunction with the boundary points are generated using appropriate meshless method such as Radial Basis Function (RBF) interpolation for the analysis.

In a simplified flow analysis approach, it is assumed that the arterial wall is stiff and wall movement is neglected. Blood is considered incompressible and homogeneous. Although blood viscosity is generally shear rate dependent, it is assumed to be Newtonian in the present computations because the non-Newtonian effect is known to be significant only when the shear rate is less than 50/second. In addition, the pulsatility of the coronary blood flow is neglected for computational economy. Thus, the simulations are based on steady flow at the present stage. Although this assumption may seem to be an over-simplification, it has been shown that there is insignificant difference in pressure drop between steady and pulsatile flows when the Reynolds number is less than 200. Moreover, flow separation characteristics do not change significantly at low Reynolds numbers (Re<500) for steady and pulsatile flows.

Within the above framework, blood flow in the coronary artery can be described by a set of transport equations for mass and momentum conservation. For an orthogonal coordinate system, the continuity (conservation of mass) equation gives:

∇·{right arrow over (V)}=0  [Equation 1]

where V is the gradient operator and V is the velocity vector. Conservation of linear momentum (steady Navier-Stokes equations) in vector form is:

ρ{right arrow over (V)}·∇{right arrow over (V)}=−∇p+μ∇ ²{right arrow over (V)}  [Equation 2]

where ∇²∇·∇, p p is the pressure, μ is the dynamic viscosity, and ρ is the density. A no-slip condition is assumed to prevail at the surface, giving:

{right arrow over (V)}_(wall)=0  [Equation 3]

For convenience, the outlet section is taken as zero gage pressure, thus:

p_(out)=0  [Equation 4]

A uniform mass flux is specified at the inlet, such that:

{right arrow over (V)}·{right arrow over (n)} _(in) =Q/A _(in)  [Equation 5]

where A_(in) is the inlet cross-sectional area, n_(in) is the unit normal vector, and Q is the volumetric flow rate.

Equations [1] and [2], coupled with the boundary conditions [3]-[5], are integrated over the luminal volume using the finite-domain scheme and a body fitted coordinate (BFC) system embodied in the PHOENICS computer code. The numerical accuracy of the results is assured by systematic grid refinement. The computations are considered to be fully converged when the maximum change in the velocity at a monitored location between two successive iterations is less than 0.1%.

Once the flow field has been computed, the results are processed to obtain final indicator functions on the luminal surface. In addition, the variation of local mean radius, R_(m), (radius of a circle of the same cross-sectional area as the lumen at a specific location) with path length, s, is determined from the reconstructed lumen data. Then, abrupt changes of radius are determined and local minimas are identified as possible locations of stenosis. Finally, the computed results and stenosis locations are displayed on the lumen surface for analysis.

The viscosity is estimated from the correlation of Walburn and Schneck:

μ=C ₁exp(C₂ H)exp(C ₄ TPMA/H ²)(C ₅{dot over (γ)})^(C) ³ ^(H)  [Equation 6]

where C₁=0.797 cP, C₂=0.0608, C₃=−0.00499, C₄=145.85 dl/g, C₅=1 s, H is Hematocrit in percent, and TPMA is total proteins minus albumin content including globulins and fiboringen. The shear rate is set to an average value defined by:

{dot over (γ)}_(c)=2V _(av) /R _(av)=2Q/(πR _(av) ³)  [Equation 7]

V_(av) is the mean velocity and R_(av) is the volume average radius of the lumen:

$\begin{matrix} {R_{av} = {\frac{1}{L}{\int_{S = 0}^{L}{R_{m}\ {s}}}}} & \left\lbrack {{Equation}\mspace{14mu} 8} \right\rbrack \end{matrix}$

An example artery segment reconstruction 1000 of an actual artery that was evaluated is shown in FIG. 10. As is apparent in the reconstruction, the lumen cross-sections are considerably irregular due to plaque growth and stenosis in the diseased arteries. Due to the complexity and irregularity of the artery segment, a fine grid system is desirable to represent the detailed structure. Grid independence tests indicate that a slab thickness of about Δs=300 μm is sufficiently accurate for the axial resolution coupled with 40 grids in the circumferential direction and 16 grids in the radial direction.

It is noted that the total number of computational nodes can exceed 100,000. This number is quite large in comparison to several other numerical studies, which usually fall in the range 6,000 to 20,000 nodes. One reason for this difference is that actual arteries are much more complex than the tube models or models generated from replicas of previous studies. Another reason is that, because the goal is accurate shear stress measurement, grid independence is performed on velocity gradients rather than velocity field, in contrast to many studies. Gradients generally have lower accuracy than field variables in numerical computations, and thus require finer grid structure for grid independence.

Since the full three-dimensional flow field cannot readily be represented in two dimensions, the velocity field is presented at four longitudinal cross-sections of the lumen at 45° intervals. To enhance the details, the lumen radius is exaggerated three fold. The resulting flow field 1100 is presented in FIG. 11 with each velocity field depicted for each of the four cross-sections 1102. It is observed that the imposed uniform inlet flow quickly develops toward parabolic and does not have much effect on the flow pattern in the remainder of the segment considered. The eccentric flow profile due to curvature at the bends and the jet-like core flow downstream of the luminal narrowings are quite evident, as indicated in the figure. In contrast to several previous numerical and experimental studies, no secondary vortex or reverse flow is observed in the diseased artery, most likely because the blood flow rates were measured at rest and are much smaller than the previous studies and because flow pulsatility is neglected in the simulations. Additionally, segments with branches were excluded.

Shear stress τ is the product of the dynamic viscosity μ, and the shear rate, {dot over (γ)}, i.e., τ=μ{dot over (γ)}. The shear rate {dot over (γ)} is related to the strain rate tensor:

γ=√{square root over (Π/2)} and Π=∥∇{right arrow over (V)}+(∇{right arrow over (V)})^(T)∥  [Equation 9]

where the superscript, T, represents the transpose operator. The shear rate calculated using Equation [9] is always positive. It thus slightly differ from previous formulations, which assumes the sign of the flow. The wall shear stress, WSS, (or endothelial shear stress) is the shear stress evaluated at the luminal surface.

FIG. 12 shows the distribution 1200 of the wall shear stress 1200. In order to show the complete lumen on a two-dimensional surface, the artery has been opened up along a longitudinal cut through an arbitrary plane (θ=0) as if it were a pathology specimen. The details are enhanced by exaggerating the luminal radius by a factor of three. In one study, the magnitude of WSS is found to be in the range 0.3-5.5 Pa (3-55 dynes/cm²) and it is within 1-2 Pa (10-20 dynes/cm²) on most parts of the surface, which is consistent with the physiological values. The eccentric flow at the curvature points cause relatively low WSS at the inner side of the curvature and relatively high WSS at the outer side of the curvature. As expected, the stenosed regions have the highest shear stresses because of flow acceleration at these narrow sections. The jet-like core flow at the downstream of the luminal narrowings cause low WSS regions because of low velocity near the lumen wall. The results indicate that in diseased arteries the shear stress pattern is very complex with closely adjoining regions of high and low wall shear stress. Studies have shown that atherogenesis is initially localized to regions of low shear stress. Thus, the regions of low shear stresses observed adjacent to the stenoses may be vulnerable to new plaque growth.

Lei et al. postulated that the wall shear stress gradient, WSSG, defined as the gradient of WSS in the direction of the luminal axis, is the single best indicator of abnormal hemodynamics influencing atherogenesis. This postulate was based on a two-dimensional simulation of a branching straight tube. WSSG can be computed to investigate the influence of arterial geometry.

Assuming the flow direction is the positive direction, WSSG can be calculated from:

$\begin{matrix} {{W\; S\; S\; G} = {\frac{{\partial W}\; S\; S}{\partial s} = {{\mu \frac{\partial\overset{.}{\gamma}}{\partial s}}^{wall}}}} & \left\lbrack {{Equation}\mspace{14mu} 10} \right\rbrack \end{matrix}$

where the direction, s, is the path length along the lumen starting at the inlet section. FIG. 13 shows the distribution of WSSG on the luminal surface. As with FIG. 12, the results are plotted on the “opened-up” lumen. WSSG exhibits abrupt changes at the stenosed regions. Specifically, it changes sign at the narrow sections but with very minimal circumferential variation. This trend appears to be primarily due to the narrowing of the lumen. Ordinarily, a sign change would be expected in WSSG profile at the locations of flow reversal. However, no flow reversal was observed in any of the coronary artery segments that were investigated.

Endothelial cell functions and atherosclerosis are related to shear stress, and disease is initiated primarily at regions of low shear stress. The arterial tree varies considerably in diameter, flow rate, and viscosity. On the other hand, wall shear stress in a healthy native artery remains in the physiological range, e.g., about 1.5 Pa (15 dynes/cm2). The changes in WSS along the artery appear mostly due to variations in local dynamics related to branching and curvatures. Thus, it can be helpful to scale (normalize) the results to reflect the effect of changes in local dynamics at different segments of the arterial tree.

To achieve this, the definition of skin friction coefficient C_(F) can be introduced. That coefficient is WSS divided by the kinetic energy of the fluid and multiplied by the local Reynolds number Re, thus:

$\begin{matrix} {{C_{F} = {2\frac{W\; S\; S}{\rho \; U_{m}^{2}}{Re}}},{{{where}\mspace{14mu} {Re}} = {2\frac{\rho \; U_{m}R_{m}}{\mu}{Re}}}} & \left\lbrack {{Equation}\mspace{14mu} 11} \right\rbrack \end{matrix}$

In equation [11], U_(m) is the mean velocity at the local cross-section. The value of C_(F) is constant and equal to 16 for fully-developed laminar flow in a straight tube (Poiseuille flow). Hence, the value of C_(F) may be a good indication of changes in local dynamics of flow affecting the wall shear stress.

FIG. 14 illustrates the distribution 1400 of C_(F) on the luminal wall for the considered case. The results exhibit local characteristics that differ from those of WSS. The maximum WSS is 36. The values of C_(p) at the narrowed locations are all around 16 and they are quite close to each other. Thus, for the investigated case, values of C_(p) are in the range 5-25 indicating that local dynamics can cause flow changes much different from those expected from Poiseuille Law, which is widely (and erroneously) used in wall shear stress calculations.

In view of the above, it can be appreciated that the location, growth, and vulnerability of arterial plaques can, in some cases, be predicted relative to the shear stresses imposed upon the plaques from blood flow. In some embodiments, the shear stress information can be used by a physician or other skilled practitioner along with the images of the plaques to evaluate how likely it is that the plaques will rupture. For example, if a given plaque (1) has a thin cap, and (2) is subjected to relatively high shear stresses, it may be concluded that the plaque is vulnerable to rupture and appropriate measures, such as invasive surgery, may be performed to prevent that rupture.

Flow-Structure Analysis

As is apparent from the foregoing, the stresses imposed upon an artery and, therefore, the possibility of plaque rupture, can be evaluated through analysis of blood flow and shear stress within the artery. As described above, the walls of the artery can be assumed to be rigid. In reality, however, healthy artery walls are flexible and elastic. Therefore, flow analysis assuming rigid walls may not provide the most accurate information regarding blood flow through the artery and/or the stresses that are imposed upon the artery walls and plaques. Notably, assuming that an entire artery segment is flexible and elastic similarly does not yield completely accurate information because plaque formation can result in the artery becoming much more plastic, particularly when the plaques calcify and harden.

In view of the above, more accurate results can be obtained by taking into account fluid flow through the artery as well as the structural properties of the artery and its plaques. When flow analysis is combined with structural analysis, plaque vulnerability can be assessed with greater accuracy. In particular, the spatial and temporal distribution of the hemodynamic variables (velocity, pressure, stresses), local hemodynamics, and plaque characteristics can be predicted and used more reliably to make determinations as to the vulnerability of a plaque to rupture.

Studies have been performed to explore the possible mechanisms that are responsible for the sudden change of a stable atherosclerotic plaque to an unstable and life-threatening atherothrombotic lesion, known as plaque tearing or disruption. For example, assessments have been made as to the type of plaques that could progress to occlusion and the other types that were likely to become vulnerable to disruption and/or thrombosis. Less obstructive plaques were found to be more lipid-rich and vulnerable to rupture than larger plaques. Furthermore, the smaller, rather than the larger, plaques were more likely to lead to acute clinical events in the case of abrupt occlusion because they were less frequently subjected to preventive therapy. Those findings suggest that plaque tearing tends to occur at the locations where the fibrous cap is thinned, and therefore weakest and most vulnerable. Those locations are coincident with the regions of the stress concentrations resulting from biomechanical and hemodynamic forces.

Among the other determinants of plaque vulnerability to rupture, structural stress is essential in understanding the stenosis tearing mechanism. Increased biomechanical stresses in the arterial wall can lead to the rupture of the fibrous cap and, subsequently, myocardial infarction or stroke. By investigating the correlation between different stages of plaque formation and patterns of mechanical stress, vulnerable plaques can be identified and treated before they rupture.

Described in the following is a study of the effects of fluid and structural properties on arteries and arterial plaques. Referring to FIG. 15, a diseased artery model 1500 was used that comprises a lumen 1502 having an obstruction 1504 that represents a stenosis. A small lipid core 1506 primarily comprising cholesterol is embedded within the stenosis 1504. The volume of the lipid core 1506 is less than 15% of the stenosis 1504. In the figure, L and Ls represent the artery segment length and the stenosis length, respectively. The nominal stenosis severity, S_(t), and eccentricity of the stenosis models, Ec, are defined as follows:

$\begin{matrix} {S_{t} = {{\left( {D_{i} - D_{s}} \right)/D_{t}} \times 100\mspace{14mu} (\%)}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack \\ {{Ec} = {\frac{e}{\left( {D_{i} - D_{s}} \right)/2} \times 100\mspace{14mu} (\%)}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack \end{matrix}$

where D_(i) and D_(s) are, respectively, the inner diameter of the occluded section and the minimum diameter of the section, and

$\begin{matrix} {e = {\frac{1}{2}\left( {D_{i} - D_{s}} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack \end{matrix}$

In the study, the model 1500 was assumed to have a total length of 110 mm, a stenosis length of 10 mm, an inner diameter of 4 mm, and a wall thickness 0.5 mm. Five models of stenosis levels of 20%, 30%, 40%, 50%, and 70% were considered, representing native (20% stenosis), moderate (30%, 40% and 50% stenosis), and severe (70% stenosis) cases. The eccentricity was assumed to be 100% in all cases to reflect common diseased arteries.

The mathematical model assumes bi-linear isotropic, incompressible material properties. Specifically, employed were the bi-linear models of Beatties et al. for the stenosis constituents, which are defined by the stress-strain curve and the two modulis E₁ and E₂ for the stress values that are less than and greater than the yield stress Y, respectively. That model was chosen because it is an optimization scheme in the sense that it gives a good approximation of the non-linear behavior of the material under internal pressure and shear stress. In addition, that model is readily implemented in multi-purpose software for simulating fluid structure interactions.

Trilateral and quadrilateral finite elements were generated for the solid and fluid parts of the arterial segment, resulting in 8505 to 9354 elements. Unlike pervious studies, the internal luminal pressure was not prescribed but rather computed from the flow module and distributed over the inner surface. The input parameters used in the study are summarized in Table 1.

TABLE 1 Principal input parameters used for the computation Inlet Velocity 0.2 m/s Outlet Gage Pressure, 0 Pa Pois- Density Kinematic Modulus Yield Modulus sion's ρ − Kg/ Viscosity E₁ − kN/ Stress E₂ − kN/ Ratio Materials m³ υ − m²/s m² Y m² θ Blood-like 1050 3.6 × 10⁻⁶ Artery 61.5 8.4 245 0.45 Plaque 483 39.6 1820 0.45 Lipid core 3.81 0.69 38.8 0.45

Previous studies have shown the prevalence of shear stress and structural stresses on plaque rupture, and the maximum principal stresses (MPS) and Von Mises stresses (VMS) were predicted. Then, by correlation with the concept of buckling in material failure study, ratios of the wall shear stresses (WSS) obtained from the flow model to each of the above structural stresses were computed for analysis. The following equilibrium and boundary conditions have been used for the artery wall models:

σ_(ij,j) ^(S)=0  [Equation 15]

σ_(ij) ^(S) ·n _(j)|inner surf=σ_(ij) ^(f) ·n _(j)|inner surf  [Equation 16]

d ^(S)inner surf|=d ^(f)|innersurf  [Equation 17]

d _(—) _(Y) ^(S)|outersurf=0  [Equation 18]

d _(—) _(X) ^(S)|inlet,outersurf=0  [Equation 19]

where d^(S)(d_(—) _(x) ^(S),d_(—) _(Y) ^(s)), d^(f), σ_(ij) ^(S), σ_(ij) ^(f) are the displacements (X and Y directions respectively) and stress tensors for solid and fluid, respectively.

The maximum principal stresses (MPS), structural maximum shear stresses (MSS), circumferential stresses (SZZ), and Von Mises stresses (VMS) were predicted. Then, the ratios of the luminal wall shear stresses (SS) obtained from the flow model to each of the above structural stresses were computed for analysis.

The study considered steady, viscous, incompressible flow in the asymmetric diseased artery model shown in FIG. 15. A lipid pool 1506 is considered due to the clinical observations that its characteristics may be closely linked to plaque vulnerability and may increase the magnitude of stress distribution over the fibrous cap. The fluid is assumed to be Newtonian at that stage. The Navier-Stokes equations for two-dimensional flow with compliant walls were solved using the CFD-ACE-GUI flow solver.

The governing equations solved in the study for the steady flow behavior are Navier-Stokes equations and can be expressed as:

Flow Direction:

$\begin{matrix} {{\nabla{\cdot \left( {\overset{\rightarrow}{V}u} \right)}} = {\frac{1}{\rho}\left\lbrack {{- \frac{\partial p}{\partial x}} + {\nabla{\cdot \left( {\mu \; {\nabla\; u}} \right)}}} \right\rbrack}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack \end{matrix}$

Transverse Direction:

$\begin{matrix} {{\nabla{\cdot \left( {\overset{\rightarrow}{V}u} \right)}} = {\frac{1}{\rho}\left\lbrack {{- \frac{\partial p}{\partial y}} + {\nabla{\cdot \left( {\mu \; {\nabla\; u}} \right)}}} \right\rbrack}} & \left\lbrack {{Equation}\mspace{14mu} 21} \right\rbrack \end{matrix}$

In those equations, p is the static pressure and τ_(ij) is the viscous stress tensor.

For boundary conditions, assumed are no-slip on the walls, no fluid penetration into the wall, and that the inlet and outlet of the segment have no axial displacement. The inlet velocity and outlet pressure are prescribed as indicated in Table 1, and are represented mathematically as:

$\begin{matrix} {{u^{\prod}} = \left( {0,0} \right)} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack \\ {{\frac{\partial u}{\partial x}^{{inlet},{outlet}}} = \left( {0,0} \right)} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack \\ {{u^{x = 0}} = {u_{in} = {0.2\mspace{14mu} m\text{/}s}}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack \\ {{p^{x = 1}} = {p_{out} = {0.0\mspace{14mu} {Nm}^{- 2}}}} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack \end{matrix}$

where u is the inflow velocity, p_(out) the pressure at the outlet, and Π is the interface between fluid and structure domains.

The viscous stresses are related to the deformation rates for the assumed Newtonian flow, thus:

$\begin{matrix} {\tau_{xx} = {{2\mu \frac{\partial\mu}{\partial x}} - {\frac{2}{3}{\mu \left( {\nabla{\cdot \overset{\rightarrow}{V}}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 26} \right\rbrack \\ {\tau_{yy} = {{2\mu \frac{\partial v}{\partial y}} - {\frac{2}{3}{\mu \left( {\nabla{\cdot \overset{\rightarrow}{V}}} \right)}}}} & \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack \\ {\tau_{xy} = {\tau_{yx} = {{\mu \frac{\partial\mu}{\partial y}} + \frac{\partial v}{\partial x}}}} & \left\lbrack {{Equation}\mspace{14mu} 28} \right\rbrack \end{matrix}$

The velocity gradients and pressure distributions were computed and recorded.

The CFD code employed for the study (CFD-ACE-GUI) used a two-way implicit coupling between the fluid and structure modules. The pressures and velocities obtained from the flow modules are sent to the stress module at every 10 iterations where deformations and stresses are calculated. Then, these deformations are sent back to the flow module, where the solution is recalculated on the new deformed geometry. Iterations are performed until convergence is obtained. The convergence criteria chosen in the study continued the iterative solution until the calculated difference between the mass inflow and mass outflow rates were negligible (less than 0.001%). Typically, the ratio of this difference to the prescribed mass inflow rate was less than 0.1%.

Fluid-Flow Analysis

An example predicted flow pattern in the lumen is presented in FIG. 16 (for a 70% stenosis level). At substantially any level of stenosis, the predicted velocity profile is parabolic upstream of the stenosis. Then, the velocity increases within the constricted section above the stenosis with the maximum value ranging from 0.34 m/s for 20% stenosis to 0.85 m/s for 70% stenosis. The parabolic profile is progressively distorted as the plaque severity increases. A small re-circulation vortex develops in the lee region of the stenosis, the size and the strength of which increase with the stenosis severity. For the most severe stenosis (70%) a second re-circulation vortex develops on the upper surface (on the upper right of FIG. 16C). The re-circulation vortices are characterized by negative velocity. Those results indicate that the flow has become fully developed over the 12D length upstream of the stenosis as expected. The maximum velocity is located within the narrowest section above the stenosis.

A flow re-circulation occurs just distal to the stenosis due to a decrease in pressure in the expanding flow channel and the no-slip condition on the surface. A second re-circulation vortex occurs for the severe (70%) stenosis case due to the combination of flow momentum and the inertia force created by the first re-circulation vortex. In other words, the pull by the first vortex creates a vacuum on the opposite side of the channel, which is rapidly filled with backward flow due to the balance of momentum. The requirement for mass and momentum conservation provides the re-circulation vortex. This re-circulation is important because it impacts the deposition of atherogenesis constituents such as low-density lipoproteins (LDL) in the lumen. The deposition mediated by both the low shear stress (SS) and the increased residence time of the constituents in the recirculation zone. This resident time increases with the size of the re-circulation vortex.

Results of the pressure study show that pressure increases on the upstream with stenosis severity ranging from 40 to 250 Pa for 20% and 70% stenosis, respectively. The pressure decreases rapidly as the velocity gradient increases on the upstream segment. The opposite effects occur on the downstream of the plaque where the pressure increases as the velocity gradient decreases. Also, it is noted that in the case of 70% stenosis, the pressure remains negative on the downstream until it recovers from the outlet. The minimum pressure is not located on the tip of the stenosis but slightly on the downstream side.

The distribution of shear stress (SS) for 20%, 40%, and 70% stenosis as a function of X/D is presented in FIG. 17. The parameter X/D on the horizontal coordinate represents the dimensionless distance along the solid-liquid interface as explained previously. The vertical double dashes represent the location of symmetric vertical plane (SP) passing through the top of stenosis.

FIG. 17 shows that the shear stress increases with the stenosis level at the upstream side of the stenosis. The wall shear stress rises monotonically to a maximum in the upstream section, then drops to the lowest value before oscillating to a constant value. The location where the stress drops from the maximum is quite distinct for the stenosis levels above 40%. The shear stress increases with stenosis severity, and its maximum occurs just before the symmetric vertical plane.

The shear stress increases at the upstream side of the lesion due to the flow acceleration resulting from channel reduction. The predicted sharp drop in the shear stress distribution and the minimum value after the drop have been observed by previous in studies. However, unlike these studies, the minimum value for the 70% stenosis model remained positive due to the physiological velocity we imposed at the inlet. The minimum stress following the drop value is located at the reattachment point downstream of the symmetric vertical plane. The shear stress (SS) is predicted on the plaque shoulder slightly upstream of the symmetric vertical plane (SP). This results is consistent with clinically observed location of plaque rupture.

Structural Analysis

The stress distributions predicted from structural analysis are illustrated in FIGS. 18A and 18B. The figures show the maximum principal stress (MPS) and Von Mises stress (VMS) for 20% and 70% stenosis levels, respectively. Those stresses describe the total stresses that a material endures for a given applied pressure. The horizontal axis X/D represents the dimensionless distance along on the solid-liquid interface. The interface considered in these plots lies just within the fibrous cap to fully account for the structural effects and stretches from the proximal to the distal ends of the stenosis (X/D=12.5 to 15.02). The vertical axis represents the predicted structural stress obtained in N/m². The vertical double dash represents the location of the symmetric vertical plane (SP) passing through the top of the stenosis.

The results indicate that, within the fibrous cap, the MPS starts with high positive values at the proximal end of the stenosis and subsequently drops rapidly to negative values. The initial high values are due to stress continuity with the upstream disease free arterial wall to the diseased segment. The incoming flow compresses the plaque proximally while the upstream wall segment is under tension. This compression produced the observed negative MPS. Peaks of MPS extension are also present in the model as shown in the graph. The main MPS peak for 70% stenoses is located on the SP, and upstream of the SP for 20% stenosis. This trend is due to the lipid pool reaction to the external compression. The MPS increases with stenosis severity on SP due to the low pressure above the plaque. Specifically, the lesion sustains important compression on its upstream side then deforms on its top where there is less resistance in order to balance the surrounding forces. The drop in the MPS curve at the end is associated with the compression of the disease-free artery wall distal of the stenosis.

The Von Mises stress (VMS) curves show three consecutive peaks: one on each side of the SP and one on the SP. The peaks on both sides of the SP increase with the stenosis severity while the peak on the SP is relatively high for 20% stenosis (70 N/m²) and significantly rises up to (˜350 N/m²) for 70% stenosis.

The maximum shear stress (MSS) and circumferential stress (SZZ) for different stenosis levels and 20% and 70% stenosis are shown in FIGS. 19A and 19B, respectively. Maximum shear stress (MSS) is meant to describe the stress in the planes 45% away from the MPS plane, where the structural shear stress is maximal. Also, circumferential stress (SZZ) describes the stress in the direction perpendicular to the model and pointing out of the screen. The horizontal axis represents the ratio X/D as explained above. The vertical axis represents the structural stress obtained in N/m².

The results indicate that, as for MPS, circumferential stress (SZZ) starts with high positive values and decrease to negative values. The positive SZZ values are due to the stress continuity with the upstream disease-free arterial wall segment to the diseased segment. Negative SZZ values are compressive stresses due to the internal pressure obliquely distributed over the diseased segment unlike on the disease-free segments where they are radial. On both sides upstream and downstream of the diseased segment, SZZ acts in the opposite direction. A peak of SZZ extension identified with positive value is also observed in the graph at the SP for stenosis greater than 30% stenosis. It is important to note that, similar to the MPS curve, SZZ rises with stenosis severity.

Similar to what has been previously shown in the Von Mises stress (VMS) results, the maximum shear stress (MSS) curve present three consecutive peaks, one on each side of the SP and one on the SP. The peaks on both sides of the SP increase with the stenosis severity, while the peak on the SP is relatively high for mild stenosis (20% stenosis) and significantly rises for severe stenosis (70% stenosis).

Fluid-Structure Interaction (FSI)

Next, appropriate fluid-structure interaction (FSI) parameters are established to characterize plaque rupture from the various stresses obtained above. The parameters identified for investigation are the stress ratios R₁ and R₂ R₁ is the ratio of shear stress to maximum principal stress (SSIMPS), and R₂ is the ratio of shear stress to Von Mises Stress (SSIVMS). FIGS. 20A and 20B show the distributions of the stress ratios R₁ and R₂ distributions.

The reasoning behind selecting the endothelial fluid shear stress ratio parameter is threefold. The first reason is the successive compression and extension of structural stress distribution in the plaque, as explained above. Second, several studies have shown that shear stress and structural stress play important roles in plaque disruption. Third, the analogy of plaque rupture with the mechanism of buckling in material failure allows one to relate endothelial shear stress in a stenosed artery to perturbation transverse force in buckling, and the internal pressure in plaque to compressive pressure in buckling.

The ratio distributions presented in FIGS. 20A and 20B are for 20% and 70% stenosis levels, respectively. The distance X is measured along the solid-liquid interface and D is the nominal diameter of the normal artery segment proximal to the lesion.

The results indicate that the stress ratio R₁, has multiple positive and negative peaks. Those peaks are located where R₁, is infinite. That trend is expected since the maximum principal stress (MPS) is zero at these locations. R₁ is negative between the two infinites prior to the mid plane SP due to the compressive MPS. Between the peak before and on the SP, R₁ is low and positive for severe stenosis (70%) but remains negative for mild stenosis (20%).

Stress ratio R₂ curves have two peaks upstream of the SP and one downstream. The first peak is more interesting to investigate for three reasons. First, it occurs on the shoulder where plaques are most likely to rupture. Second, the first peak's base is larger than the others. Third, the first peak varies with the stenosis severity. A close look at both ratios reveals that, at the location of the first peak of R₂, the ratio R₁ changes with the stenosis level.

Stress ratios R₃ and R₄ distributions are presented in FIGS. 21A and 21B. R₃ is the ratio of wall shear stress to maximum shear stress (SS/MSS), and R₄ is the ratio of wall shear stress to circumferential stress (SS/SZZ). As for the cases above, the ratio distributions presented below are for two stenosis levels: 20% and 70% stenosis corresponding to the FIGS. 21A and 21B, respectively.

The results shown in FIGS. 21A and 21B indicate that, similar to R₁, R₄, multiple positive and negative peaks are evident. Those peaks are located where R₄ is infinite. This trend is expected since circumferential stress (SZZ) is zero at these locations. Between the two, R₄ infinites prior to the mid plane SP, and R₄ is negative due to the compressive SZZ. At the vicinity of the SP, R₄ remains almost unchanged and close to zero. After the SP, R₄ for severe (70%) stenosis becomes discontinuous and changes sign at approximately ⅓ the distance from the base of the lesion, downstream of the SP.

The stress ratio R₃ curves have similarities with R₂, and the characteristics previously cited for R₂ can be applied to R₃. In addition, it is noted that, at the location of the first peak of the ratio R₃, the stress ratio R₄ changes with the stenosis level.

The fluid structure interaction parameters that were computed to characterize the stenotic plaque vulnerability are summarized in FIG. 22. In that figure, the horizontal axis represents the percentage of the stenosis, and the vertical axis represents the monitored stress ratio. Specifically, the plots represent the values of R₁ and R₄ at monitored locations for stenosis levels of 20%, 30%, 40%, 50%, and 70% stenosis. The monitored locations were the X/D locations where the first R₂ and R₃ maximum occur upstream of the mid plan (SP) in FIGS. 20 and 21, respectively. Those locations were selected because they are situated on plaque shoulder where plaque rupture most likely takes place, and the magnitude of the stress ratios varies with stenosis severity.

R ₁ =|R ₁{(X/D)_(R2) _(max) }|  [Equation 29]

R ₄ =|R ₄{(X/D)_(R3) _(Max) }|  [Equation 30]

The monitored R₁ and R₄ values are presented in FIG. 22 for comparison.

The results show that although the two methods to characterize plaque rupture R₁ _(—) _(Monitored) and R₄ _(—) _(Monitored) exhibit the same trend, R₁ _(—) _(Monitored) is consistently larger than R₄ _(—) _(Monitored). In general, the predicted FSI indices are low for both mild (e.g. 20%) and severe (e.g. 70%) stenosis. Interestingly, those indices reach a maximum between the extreme stenosis levels at typically approximately 40% to 45% stenosis. This stenosis range can be considered prone to rupture as it is consistent with medical observation. In other words, this result indicates that the FSI indices investigated here can serve to characterize plaque vulnerability. Plaques typically remain asymptomatic until the stenosis level exceeds about 70% of the lumen. However, it has been suggested that nearly 68% of myocardial infarction patients had less than 50% stenosis. The results presented here suggest lipid-laden plaques of 40% to 45% stenosis may be vulnerable to sudden rupture of the fibrous cap.

By carefully monitoring the stress ratio either R₁ or R₄ at the location of maximum stress ratio R₂ or R₃, respectively, an experimental study can establish the stability value of R₁ _(—) _(Cr), or R₄ _(—) _(Cr) (critical value) for atheroma rupture. These critical stress ratios combine the interaction of flow and structural parameters on plaque characteristic, and are referred to as the flow-structure interaction (FSI) stability indices.

The FSI indices can be to be associated with the plaque location where the stress ratios become infinite in order for the indices to be more meaningful. Specifically, if there is no discontinuity for either R₁ or R₄ distribution, the plaque is likely to be stable. Likewise, if there is discontinuity for R₁ or R₄ and their magnitude at the location of maximum R₂ or R₃, respectively, is smaller than a threshold (e.g., determined experimentally), the plaque is likely stable. Otherwise, the plaque can be deemed unstable and vulnerable to rupture.

As with the flow analysis described above, the arterial plaques rupture can, in some cases, be predicted relative to the shear stresses imposed upon the plaques from blood flow and relative to the structural characteristics of the plaques. In some embodiments, the shear stress information and structural information can be used by a physician or other skilled practitioner along with the images of the plaques to evaluate how likely it is that the plaques will rupture. For example, if a given plaque (1) has a thin cap, (2) is subjected to relatively high shear stresses, and (3) has a structure that is likely to fail, it may be concluded that the plaque is vulnerable to rupture and appropriate measures, such as invasive surgery, may be performed to prevent that rupture. In other embodiments, a physician or other skilled practitioner can make a determination as to plaque vulnerability to rupture in view of a fluid-structure interaction index that is automatically generated by the evaluation system. In such a case, the vulnerability determination may be simplified and/or made with greater consistency. Establishing such an index may require consideration of other facts of plaque vulnerability such as the detailed plaque characteristics including fibrious cap thickness, lipid pool size and eccentricity, calcium composition, and so forth.

As noted above, while particular embodiments have been described in this disclosure, alternative embodiments are possible. All alternative embodiments are intended to be covered by the present disclosure. 

1. A method for evaluating a vessel comprising: capturing optical coherence tomography (OCT) images of the vessel; analyzing the OCT images to generate a three-dimensional model of the vessel; and conducting analysis on data associated with the three-dimensional model.
 2. The method of claim 1, wherein capturing OCT images of the vessel comprises capturing OCT images of the vessel with an optical catheter positioned within the vessel.
 3. The method of claim 1, further comprising capturing fluorescence spectroscopy images of the vessel.
 4. The method of claim 1, wherein conducting analysis comprises conducting flow analysis in relation to fluid flow through the vessel.
 5. The method of claim 1, wherein conducting analysis comprises conducting structural analysis in relation to walls of the vessel.
 6. The method of claim 1, wherein the vessel is an artery and conducting analysis comprises conducting analysis on the artery to determine the vulnerability of plaques within the artery to rupture.
 7. A computer-readable medium comprising a system for evaluating a vessel, the computer-readable medium, comprising: logic configured to capture optical coherence tomography (OCT) images of the vessel; logic configured to analyze the OCT images to generate a three-dimensional model of the vessel; and logic configured to conduct analysis on data associated with the three-dimensional model.
 8. The computer-readable medium of claim 7, wherein the logic configured to capture OCT images of the vessel comprises logic configured to capture OCT images of the vessel with an optical catheter positioned within the vessel.
 9. The computer-readable medium of claim 7, further comprising logic configured to capture fluorescence spectroscopy images of the vessel.
 10. The computer-readable medium of claim 7, wherein the logic configured to conduct analysis comprises logic configured to conduct flow analysis in relation to fluid flow through the vessel.
 11. The computer-readable medium of claim 7, wherein the logic configured to conduct analysis comprises logic configured to conduct structural analysis in relation to walls of the vessel.
 12. The computer-readable medium of claim 7, wherein the vessel is an artery and the logic configured to conduct analysis comprises logic configured to conduct analysis on the artery to determine the vulnerability of plaques within the artery to rupture.
 13. A method for evaluating a vessel comprising: capturing images of the vessel by an optical catheter positioned within the vessel; simultaneously determining a position and orientation of the catheter with information generated by a tracking device of the catheter; analyzing the images to generate a three-dimensional model of the vessel; and conducting analysis on data associated with the three-dimensional model.
 14. The method of claim 13, wherein capturing images of the vessel comprises capturing optical coherence tomography (OCT) images of the vessel.
 15. The method of claim 14, wherein capturing images of the vessel further comprises capturing fluorescence spectroscopy images of the vessel.
 16. The method of claim 13, wherein conducting analysis comprises conducting flow analysis in relation to fluid flow through the vessel.
 17. The method of claim 13, wherein conducting analysis comprises conducting structural analysis in relation to walls of the vessel.
 18. The method of claim 13, wherein the vessel is an artery and conducting analysis comprises conducting analysis on the artery to determine the vulnerability of plaques within the artery to rupture.
 19. A computer-readable medium comprising a system for evaluating a vessel, the computer-readable medium comprising: logic configured to process images of the vessel captured by an optical catheter positioned within the vessel; logic configured to simultaneously determine a position and orientation of the catheter with information generated by a tracking device provided within the catheter; logic configured to analyze the images to generate a three-dimensional model of the vessel; and logic configured to conduct analysis on data associated with the three-dimensional model.
 20. The computer-readable medium of claim 19, wherein logic configured to process images of the vessel comprises logic configured to process optical coherence tomography (OCT) images of the vessel.
 21. The computer-readable medium of claim 20, wherein the logic configured to process images of the vessel further comprises logic configured to process fluorescence spectroscopy images of the vessel captured by the catheter.
 22. The computer-readable medium of claim 19, wherein the logic configured to conduct analysis comprises logic configured to conduct flow analysis in relation to fluid flow through the vessel.
 23. The computer-readable medium of claim 19, wherein the logic configured to conducting analysis comprises logic configured to conduct structural analysis in relation to walls of the vessel.
 24. The computer-readable medium of claim 19, wherein the vessel is an artery and the logic configured to conduct analysis comprises logic configured to conduct analysis on the artery to determine the vulnerability of plaques within the artery to rupture.
 25. An optical catheter comprising: an internal optical system configured to capture images of a vessel in which the catheter is positioned; and a tracking device that determines the position and orientation of the catheter within the vessel simultaneous of image capture.
 26. The catheter of claim 25, wherein the tracking device is capable of collecting positional and orientation data within 6 degrees of freedom.
 27. The catheter of claim 25, wherein the catheter is configured to capture images about an axis of the catheter along 360°.
 28. The catheter of claim 25, wherein the catheter is sized and configured to be positioned within a coronary artery and capture images of the arterial walls and plaques formed within the artery.
 29. The catheter of claim 25, wherein the catheter is configured to capture optical coherence tomography (OCT) images of the vessel.
 30. The catheter of claim 29, wherein the catheter is further configured to capture fluorescence spectroscopy images of the vessel.
 31. A method for evaluating a vessel comprising: capturing images of the vessel; analyzing the images to generate a three-dimensional model of the vessel; and conducting analysis on data associated with the three-dimensional model, the analysis including flow analysis in relation to fluid flow through the vessel and structural analysis in relation to walls of the vessel.
 32. The method of claim 31, wherein capturing images of the vessel comprises capturing optical coherence tomography (OCT) images of the vessel with the optical catheter.
 33. The method of claim 32, wherein capturing images of the vessel further comprises capturing fluorescence spectroscopy images of the vessel.
 34. The method of claim 31, wherein the vessel is an artery and conducting analysis comprises conducting the flow analysis and the structural analysis to determine the vulnerability of plaques within the artery to rupture.
 35. The method of claim 31, wherein conducting analysis further comprises developing a flow-structure index that is indicative of likelihood of plaque rupture.
 36. The method of claim 31, wherein conducting the flow analysis and the structural analysis is performed in an iterative process in which the structural analysis influences the flow analysis and vice versa.
 37. A computer-readable medium comprising a system for evaluating a vessel comprising: logic configured to capture images of the vessel; logic configured to analyze the images to generate a three-dimensional model of the vessel; and logic configured to conduct analysis on data associated with the three-dimensional model, the analysis including flow analysis in relation to fluid flow through the vessel and structural analysis in relation to walls of the vessel.
 38. The computer-readable medium of claim 37, wherein the logic configured to capture images of the vessel comprises logic configured to capture optical coherence tomography (OCT) images of the vessel with the optical catheter.
 39. The computer-readable medium of claim 38, wherein the logic configured to capture images of the vessel further comprises logic configured to capture fluorescence spectroscopy images of the vessel.
 40. The computer-readable medium of claim 37, wherein the vessel is an artery and the logic configured to conduct analysis comprises logic configured to conduct the flow analysis and the structural analysis to determine the vulnerability of plaques within the artery to rupture.
 41. The computer-readable medium of claim 37, wherein the logic configured to conduct analysis further comprises logic configured to develop a flow-structure index that is indicative of likelihood of plaque rupture.
 42. The computer-readable medium of claim 37, wherein the logic configured to conduct the flow analysis and the structural analysis performs the analysis in an iterative process in which the structural analysis influences the flow analysis and vice versa. 